Determining the flow rate of air in a computer system

ABSTRACT

Some embodiments of the present invention provide a system that determines a flow rate of air along an airflow path in a computer system. During operation the system monitors a first temperature profile from a first temperature sensor located in a first position in the airflow path, and monitors a second temperature profile from a second temperature sensor located in a second position in the airflow path, wherein the first position is upstream in the airflow path from the second position, and wherein the first position and the second position are separated by a predetermined distance along the airflow path. Next, the system computes a cross-power spectral density based on the first temperature profile and the second temperature profile. Then, the system determines a flow rate of air in the computer system based on the cross-power spectral density.

BACKGROUND

1. Field

The present invention generally relates to techniques for characterizinga computer system. More specifically, the present invention relates to amethod and an apparatus that determines a flow rate of air along anairflow path through a computer system.

2. Related Art

To provide sufficient cooling, designers of computer systems are ofteninterested in the flow rate of air through a computer system, which canbe measured in linear feet per minute (LFM) or in cubic feet per minute(CFM). These parameters can take a great amount of time to measureexperimentally and may be difficult to compute using methods such ascomputational fluid dynamics modeling due to potentially complex andtortuous air flow paths in the computer system, in addition to the factthat the density of air can change as the air changes temperature whileit travels through the computer system. Additionally, directly measuringLFM and CFM in the field using mechanical sensors may require periodicmanual recalibration of the sensors used over a long period of time andcan be impractical for large populations of servers in datacenters.

Hence, what is needed is a method and system that determines a flow rateof air through a computer system without the above-described problems.

SUMMARY

Some embodiments of the present invention provide a system thatdetermines a flow rate of air along an airflow path in a computersystem. During operation the system monitors a first temperature profilefrom a first temperature sensor located in a first position in theairflow path, and monitors a second temperature profile from a secondtemperature sensor located in a second position in the airflow path,wherein the first position is upstream in the airflow path from thesecond position, and wherein the first position and the second positionare separated by a predetermined distance along the airflow path. Next,the system computes a cross-power spectral density based on the firsttemperature profile and the second temperature profile. Then, the systemdetermines a flow rate of air in the computer system based on thecross-power spectral density.

In some embodiments, the system generates an alarm based on the flowrate of air in the computer system.

In some embodiments, determining the airflow rate includes determining atransit time based on a phase-frequency slope of the cross-powerspectral density.

In some embodiments, determining the flow rate of air includesdetermining a cross-sectional flow area for the air flow path, anddetermining a cubic feet per minute flow rate based on thecross-sectional flow area and the flow rate of air.

In some embodiments, determining the flow rate includes calibrating themeasurement of the flow rate by determining the flow rate of airassociated with specific fan speeds in a set of computer fan speeds.

In some embodiments, calibrating the measurement of the flow rate of airincludes determining a cross-sectional flow area for the air flow.

In some embodiments, while determining the flow rate the system firstmonitors a set of temperature profiles from a set of temperature sensorslocated in a set of positions in the airflow path in the computersystem, wherein the positions are separated by a set of predetermineddistances along the airflow path. Next, the system computes a set ofcross-power spectral densities based on pairs of temperature profiles inthe set of temperature profiles from pairs of temperature sensors in theset of temperature sensors. Then, the system determines the flow ratebased on the set of cross-power spectral densities for each pair oftemperature profiles, and the predetermined distance for each pair oftemperature sensors.

In some embodiments, determining a flow rate of air in the computersystem based on the cross-power spectral density includes determining anaverage of the cross-power spectral density over a predetermined timeperiod.

In some embodiments, prior to computing the cross-power spectraldensity, the system transforms the first temperature profile into afirst temperature profile frequency domain representation, andtransforms the second temperature profile into a second temperatureprofile frequency domain representation.

In some embodiments, monitoring the first temperature profile and thesecond temperature profile includes systematically monitoring andrecording a set of performance parameters of the computer system,wherein the recording process keeps track of the temporal relationshipsbetween events in different performance parameters.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 represents a system that determines a flow rate of air along anairflow path in a computer system in accordance with some embodiments ofthe present invention.

FIG. 2 presents a flow chart illustrating a process that determines aflow rate of air along an airflow path in a computer system inaccordance with some embodiments of the present invention.

DETAILED DESCRIPTION

The following description is presented to enable any person skilled inthe art to make and use the disclosed embodiments, and is provided inthe context of a particular application and its requirements. Variousmodifications to the disclosed embodiments will be readily apparent tothose skilled in the art, and the general principles defined herein maybe applied to other embodiments and applications without departing fromthe spirit and scope of the present description. Thus, the presentdescription is not intended to be limited to the embodiments shown, butis to be accorded the widest scope consistent with the principles andfeatures disclosed herein.

The data structures and code described in this detailed description aretypically stored on a computer-readable storage medium, which may be anydevice or medium that can store code and/or data for use by a computersystem. This includes, but is not limited to, volatile memory,non-volatile memory, magnetic and optical storage devices such as diskdrives, magnetic tape, CDs (compact discs), DVDs (digital versatilediscs or digital video discs), or other media capable of storingcomputer-readable media now known or later developed.

The methods and processes described in the detailed description sectioncan be embodied as code and/or data, which can be stored in acomputer-readable storage medium as described above. When a computersystem reads and executes the code and/or data stored on thecomputer-readable storage medium, the computer system performs themethods and processes embodied as data structures and code and storedwithin the computer-readable storage medium.

Furthermore, the methods and processes described below can be includedin hardware modules. For example, the hardware modules can include, butare not limited to, application-specific integrated circuit (ASIC)chips, field-programmable gate arrays (FPGAs), and otherprogrammable-logic devices now known or later developed. When thehardware modules are activated, the hardware modules perform the methodsand processes included within the hardware modules.

FIG. 1 represents a system that determines a flow rate of air along anairflow path in a computer system in accordance with some embodiments ofthe present invention. Computer system 100 includes fan 102A and fan102B generating air flow along airflow path 104 and between board 106and power supply 108. Computer system 100 also includes temperaturesensor 110A and temperature sensor 110B coupled to flow-ratedetermination mechanism 112. Furthermore, flow-rate determinationmechanism 112 includes temperature-sensor monitor 114, cross-powerspectral-density (CPSD) module 116 and flow-rate module 118.

Computer system 100 can include but is not limited to a server, a serverblade, a datacenter server, a field-replaceable unit, an enterprisecomputer, or any other computation system that includes one or moreprocessors and one or more cores in each processor.

Fan 102A and fan 102B can be any type of fan implemented in anytechnology that creates airflow along airflow path 104 in computersystem 100. Note that in some embodiments there may be more or fewerfans in computer system 100 that create airflow along airflow path 104.Also note that board 106 and power supply 108 are depicted in computersystem 100 for exemplary purposes only to represent internal structurein computer system 100 that may help shape airflow path 104. In someembodiments board 106 and/or power supply unit 108 may be removed,repositioned or replaced by other devices, subcomponents or systems incomputer system 100.

Airflow path 104 depicts the flow of air in computer system 100resulting from air flow generated by fan 102A and fan 102B insidecomputer system 100 around board 106 and power supply 108. Note that theparticular path of airflow path 104 depicted in FIG. 1 is for exemplarypurposes only and in other embodiments may take other paths throughcomputer system 100 without departing from the present invention.

Temperature sensor 110A and temperature sensor 110B sense thetemperature profile of air in airflow path 104 and are located apredetermined distance apart along airflow path 104. Temperature sensor110A and temperature sensor 110B can include any type oftemperature-sensitive sensor including but not limited to a discretetemperature-sensing device, or a temperature-sensing device integratedinto a computer system component. Temperature sensor 110A andtemperature sensor 110B may be mechanical, electrical, optical, or anycombination thereof, and may be implemented in any technology now knownor later developed. In some embodiments, temperature sensor 110A andtemperature sensor 110B are coupled to one or more data buses incomputer system 100 to enable communication of the sensed temperaturedata within and out of computer system 100.

Temperature-sensor monitor 114 can be any device that can monitortemperature profiles sensed by temperature sensor 110A and temperaturesensor 110B. Temperature-sensor monitor 114 can be implemented in anycombination of hardware and software. In some embodiments,temperature-sensor monitor 114 operates on computer system 100. In otherembodiments, temperature-sensor monitor 114 operates on one or moreservice processors. In still other embodiments, temperature-sensormonitor 114 is located inside of computer system 100. In yet otherembodiments, temperature-sensor monitor 114 operates on a separatecomputer system. In some embodiments, temperature-sensor monitor 114includes a method or apparatus for monitoring and recording computersystem performance parameters as set forth in U.S. Pat. No. 7,020,802,entitled “Method and Apparatus for Monitoring and Recording ComputerSystem Performance Parameters,” by Kenny C. Gross and Larry G. Votta,Jr., issued on 28 March 2006, which is hereby fully incorporated byreference.

CPSD module 116 can be any device that can generate a CPSD from themonitored temperature profiles received from temperature-sensor monitor114 in accordance with embodiments of the present invention. CPSD module116 can be implemented in any combination of hardware and software. Insome embodiments, CPSD module 116 operates on computer system 100. Inother embodiments, CPSD module 116 operates on one or more serviceprocessors. In still other embodiments, CPSD module 116 is locatedinside of computer system 100. In yet other embodiments, CPSD module 116operates on a separate computer system.

Flow-rate module 118 is any device that can receive input from CPSDmodule 116 and determine the flow rate of air along airflow path 104 inaccordance with embodiments of the present invention. Flow-rate module118 can be implemented in any combination of hardware and software. Insome embodiments, flow-rate module 118 operates on computer system 100.In other embodiments, flow-rate module 118 operates on one or moreservice processors. In still other embodiments, flow-rate module 118 islocated inside of computer system 100. In yet other embodiments,flow-rate module 118 operates on a separate computer system.

Some embodiments of the present invention operate as follows. As airflows in computer system 100 along airflow path 104, temperature sensor110A and temperature sensor 110B sense the temperature profile of theair in airflow path 104 over time. The temperature profiles fromtemperature sensor 110A and temperature sensor 110B are monitored bytemperature-sensor monitor 114. The monitored temperature profiles aresent to CPSD module 116. CPSD module 116 then computes the cross-powerspectral density of the temperature profiles monitored by temperaturesensor 110A and temperature sensor 110B.

CPSD module 116 can implement any method or apparatus now known or laterdeveloped to generate the CPSD without departing from the presentinvention. In some embodiments, CPSD module 116 transforms thetemperature profiles received from temperature-sensor monitor 114 intofrequency domain representations, then computes the CPSD using thefrequency domain representation of the temperature profile fromtemperature sensor 110A and the frequency domain representation of thetemperature profile from temperature sensor 110B. In some embodiments,transforming the temperature profiles from the time domain to thefrequency domain involves using a Fourier transform which can includebut is not limited to a discrete Fourier transform such as a fastFourier transform (FFT). In other embodiments, other transform functionscan be used, including, but not limited to, a Laplace transform, aZ-transform, and any other transform technique now known or laterdeveloped. In some embodiments, the CPSD is computed by generating thecomplex conjugate of one of the frequency domain representations of onetemperature profile and multiplying it by the other frequency domainrepresentation of the other temperature profile.

In other embodiments, the CPSD is computed by first computing thecross-correlation of the time-domain representations of the temperatureprofiles from temperature sensor 110A and temperature sensor 110B. Then,the CPSD is generated by computing the frequency domain representationof the cross-correlation. In some embodiments, transforming thecross-correlation from the time domain to the frequency domain involvesusing a Fourier transform which can include but is not limited to adiscrete Fourier transform such as an FFT. In other embodiments, othertransform functions can be used, including, but not limited to, aLaplace transform, a Z-transform, and any other transform technique nowknown or later developed.

Flow-rate module 118 then receives the CPSD from CPSD module 116. Insome embodiments, flow-rate module 118 receives the product of theFourier transform of one temperature profile multiplied by the complexconjugate of the Fourier transform of the other temperature profile.Flow-rate module 118 then determines the slope of the CPSD phase (indegrees) versus frequency (in hertz). The transit time in seconds forthe air flow from temperature sensor 110A to temperature sensor 110B isthen determined by dividing the slope of the CPSD phase vs. frequency by360 degrees. The LFM is then determined by dividing the predetermineddistance between temperature sensor 110A and temperature sensor 110B bythe transit time. The CFM is then determined by multiplying the LFM by across-sectional area for computer system 100.

For example, in some embodiments, a time-series of temperaturemeasurements (a temperature profile) monitored by temperature-sensormonitor 114 from temperature sensor 110A is fast Fourier transformed byCPSD module 116. Additionally a time-series of temperature measurements(a temperature profile) monitored by temperature-sensor monitor 114 fromtemperature sensor 110B is fast Fourier transformed and the complexconjugate is generated by CPSD module 116. The CPSD is then generated byCPSD module 116 by multiplying the FFT of the temperature profile fromtemperature sensor 110A by the complex conjugate of the FFT oftemperature profile from temperature sensor 110B. The resulting CPSD canbe represented as a magnitude portion that is a function of frequencyand a phase portion that is a function of frequency. The phase portionof the CPSD can be represented as a phase angle in degrees versusfrequency in hertz which has a slope in degrees/hertz (degrees·seconds).The slope is then divided by 360 degrees to generate the transit time inseconds for the air flow from temperature sensor 110A to temperaturesensor 110B. Then, the LFM is determined by dividing the predetermineddistance between temperature sensor 110A and temperature sensor 110B bythe transit time, and the CFM is determined by multiplying the LFM bythe cross-sectional area for computer system 100.

Note that the predetermined distance between temperature sensor 110A andtemperature sensor 110B, and/or the cross-sectional area of computersystem 100 can be determined by analysis of the design of computersystem 100, during calibration testing of computer system 100, or by anyother suitable method. For example, during calibration testing ofcomputer system 100 prior to putting computer system 100 in the field,the predetermined distance between temperature sensor 110A andtemperature sensor 110B, and/or the cross-sectional area of computersystem 100 can be determined using air-flow meters to measure the LFMand CFM and the above process to determine the transit time. Thepredetermined distance between temperature sensor 110A and temperaturesensor 110B can be determined by multiplying the measured LFM by thetransit time, and the cross-sectional area can be determined by dividingthe measured CFM by the measured LFM. Additionally, in some embodimentsduring the calibration period, the LFM and CFM are determined for a setof speeds for fan 102A and fan 102B. In these embodiments, flow-ratedetermination mechanism 112 monitors the speed of fan 102A and the speedof fan 102B. The predetermined distance and area as a function of fanspeeds of fan 102A and fan 102B are then used by flow-rate module 118 todetermine the LFM and CFM during operation of flow-rate determinationmechanism 112.

In some embodiments, flow-rate module 118 generates an alarm based onthe determined flow rate of air along airflow path 104. For example, insome embodiments, flow-rate module 118 receives information fromcomputer system 100 related to the fan speeds of fan 102A and fan 102B.Flow-rate module 118 then generates an alarm if the LFM determined byflow-rate module 118 falls below a predetermined value. Thepredetermined value may be determined based information including butnot limited to one or more of: a minimum LFM considered safe forcomputer system 100, or an LFM that departs by a fix amount orpercentage from the LFM measured during the calibration period discussedabove based on the monitored fan speeds. Note that in some embodimentsthe alarm generated by flow-rate module 118 can include but is notlimited to one or more of the following: generating a maintenancerequest, or generating a notification (such as an automated email,telephone call, page, turning on a light, or generating a sound).

In some embodiments, flow-rate module 118 averages the CPSDs receivedfrom CPSD module 116 over a predetermined time period prior todetermining the LFM or CFM using the above processes. In someembodiments, the predetermined time period is determined based oninformation including but not limited to one or more of: the rate atwhich temperature profiles are monitored by temperature-sensor monitor114, the rate at which the speed of fan 102A and/or fan 102B is changed,or the rate of change of any other thermal process in computer system100.

In some embodiments fan 102A and fan 102B are replaced by a set of fansin airflow path 104 in computer system 100. Temperature-sensor monitor114 monitors the temperature profile from fans in the set of fans. CPSDmodule 116 then determines the CPSD for temperature profiles from pairsof temperature sensors in the set of temperature sensors using one ormore techniques as described above. Flow-rate module 118 then determinesthe transit time for each pair of temperature sensors using techniquesdescribed above. The LFM is then determined based on the predetermineddistance between each pair of temperature sensors, and the CFM isdetermined from the LFM based on the cross-sectional area determined forthe air flow between the pairs of temperature sensors. Note that asdescribed above, the predetermined distance and cross-sectional areabetween each pair of temperature sensors in the pair of temperaturesensors can be determined as described above based on techniquesincluding but not limited to directly computing the predetermineddistance and effective cross-sectional area, or determining them usingmeasurements from a calibration period in which the LFM and CFM aredirectly measured.

FIG. 2 presents a flow chart illustrating a process that determines aflow-rate of air along an airflow path in a computer system inaccordance with some embodiments of the present invention. First,temperature-monitoring software is installed on the computer system(step 202). Note that the computer system contains a set of temperaturesensors in the airflow path being measured. Then, temperature profilesare monitored from each temperature sensor in the set of temperaturesensors (step 204). Next, a pair of temperature sensors in the set oftemperature sensors is selected that has not yet been selected (step206). The CPSD of the temperature profiles from the two selectedtemperature sensors is determined as described above, and the slope ofthe phase versus frequency for the CPSD is determined (step 208). Thetransit time is then determined using the slope as discussed above (step210). For example, if the slope of the phase in degrees versus thefrequency in hertz of the CPSD is determined, the transit time inseconds is the slope divided by 360 degrees.

Next, the LFM is computed from the transit time by dividing the distancebetween the pair of temperature sensors by the transit time (step 212).In some embodiments, the distance between sensors is determined bydirect measurement. In other embodiments, the distance is determinedbased on a calibration period during which the LFM is directly measuredand the transit time is measured as describe above. The distance betweenthe sensors is then determined by multiplying the LFM by the transittime. Note that during the calibration period, measurements may be takenfor a range of fan speeds including a range from a zero fan speed to themaximum fan speed in order to determine the distance between thesensors.

Then, if all pairs of temperature sensors have not yet been selected andan LFM computed for each pair (step 214), the process returns to step206. If all pairs of temperature sensors have been selected and an LFMhas been computed for each pair (step 214), then the average LFM isdetermined by computing the average of the LFMs computed for each pairof temperature sensors in the set of temperature sensors (step 216). TheCFM is determined by multiplying the LFM by the flow area (step 216). Insome embodiments, the flow area is determined by direct measurement. Inother embodiments, the flow area is determined based on a calibrationperiod during which the CFM and LFM are directly measured and flow areais determined by dividing the CFM by the LFM. Note that during thecalibration period, measurements may be taken for a range of fan speedsincluding a range from a zero fan speed to the maximum fan speed inorder to determine the flow area as a function of fan speed.

The foregoing descriptions of embodiments have been presented forpurposes of illustration and description only. They are not intended tobe exhaustive or to limit the present description to the formsdisclosed. Accordingly, many modifications and variations will beapparent to practitioners skilled in the art. Additionally, the abovedisclosure is not intended to limit the present description. The scopeof the present description is defined by the appended claims.

1. A method for determining a flow rate of air along an airflow path ina computer system, the method comprising: monitoring a first temperatureprofile from a first temperature sensor located in a first position inthe airflow path in the computer system; monitoring a second temperatureprofile from a second temperature sensor located in a second position inthe airflow path in the computer system, wherein the first position isupstream in the airflow path from the second position, and wherein thefirst position and the second position are separated by a predetermineddistance along the airflow path; computing a cross-power spectraldensity based on the first temperature profile and the secondtemperature profile; determining a flow rate of air in the computersystem based on the cross-power spectral density; and generating analarm based on the flow rate of air in the computer system.
 2. Themethod of claim 1, wherein: determining the airflow rate includesdetermining a transit time based on a phase-frequency slope of thecross-power spectral density.
 3. The method of claim 1, whereindetermining the flow rate of air includes: determining a cross-sectionalflow area for the air flow path; and determining a volume per minuteflow rate based on the cross-sectional flow area and the flow rate ofair.
 4. The method of claim 1, wherein determining the flow rateincludes calibrating the determination of the flow rate by determiningthe flow rate of air in the computer system associated with specific fanspeeds in a set of computer fan speeds.
 5. The method of claim 4,wherein calibrating the determination of the flow rate of air in thecomputer system includes determining a cross-sectional flow area for theairflow.
 6. The method of claim 1, wherein monitoring the first andsecond temperature profiles includes monitoring a set of temperatureprofiles from a set of temperature sensors located in a set of positionsin the airflow path in the computer system, wherein positions in the setof positions are separated by a set of predetermined distances along theairflow path; wherein computing the cross-power spectral densityincludes computing a set of cross-power spectral densities based onpairs of temperature profiles in the set of temperature profiles frompairs of temperature sensors in the set of temperature sensors; andwherein determining the flow rate includes determining the flow ratebased on the set of cross-power spectral densities for each pair oftemperature profiles, and the predetermined distance for each pair oftemperature sensors.
 7. The method of claim 1, wherein determining theflow rate of air in the computer system based on the cross-powerspectral density includes determining an average of the cross-powerspectral density over a predetermined time period.
 8. The method ofclaim 1, wherein prior to computing the cross-power spectral density,the method further comprises transforming the first temperature profileinto a first temperature profile frequency domain representation, andtransforming the second temperature profile into a second temperatureprofile frequency domain representation.
 9. The method of claim 1,wherein monitoring the first temperature profile and the secondtemperature profile includes systematically monitoring and recording aset of temperature profiles of the computer system; and wherein therecording process keeps track of the temporal relationships betweenevents in different temperature profiles.
 10. A computer-readablestorage medium storing instructions that when executed by a computercause the computer to perform a method for determining a flow rate ofair along an airflow path in a computer system, the method comprising:monitoring a first temperature profile from a first temperature sensorlocated in a first position in the airflow path in the computer system;monitoring a second temperature profile from a second temperature sensorlocated in a second position in the airflow path in the computer system,wherein the first position is upstream in the airflow path from thesecond position, and wherein the first position and the second positionare separated by a predetermined distance along the airflow path;computing a cross-power spectral density based on the first temperatureprofile and the second temperature profile; determining a flow rate ofair in the computer system based on the cross-power spectral density;and generating an alarm based on the flow rate of air in the computersystem.
 11. The computer-readable storage medium of claim 10, whereindetermining the airflow rate includes determining a transit time basedon a phase-frequency slope of the cross-power spectral density.
 12. Thecomputer-readable storage medium of claim 10, wherein determining theflow rate of air includes: determining a cross-sectional flow area forthe air flow path; and determining a volume per minute flow rate basedon the cross-sectional flow area and the flow rate of air.
 13. Thecomputer-readable storage medium of claim 10, wherein determining theflow rate includes calibrating the determination of the flow rate bydetermining the flow rate of air in the computer system associated withspecific fan speeds in a set of computer fan speeds.
 14. Thecomputer-readable storage medium of claim 13, wherein calibrating thedetermination of the flow rate of air in the computer system includesdetermining a cross-sectional flow area for the airflow.
 15. Thecomputer-readable storage medium of claim 10, wherein monitoring thefirst and second temperature profiles includes monitoring a set oftemperature profiles from a set of temperature sensors located in a setof positions in the airflow path in the computer system, whereinpositions in the set of positions are separated by a set ofpredetermined distances along the airflow path; wherein computing thecross-power spectral density includes computing a set of cross-powerspectral densities based on pairs of temperature profiles in the set oftemperature profiles from pairs of temperature sensors in the set oftemperature sensors; and wherein determining the flow rate includesdetermining the flow rate based on the set of cross-power spectraldensities for each pair of temperature profiles, and the predetermineddistance for each pair of temperature sensors.
 16. The computer-readablestorage medium of claim 10, wherein determining the flow rate of air inthe computer system based on the cross-power spectral density includesdetermining an average of the cross-power spectral density over apredetermined time period.
 17. The computer-readable storage medium ofclaim 10, wherein prior to computing the cross-power spectral density,the method further comprises transforming the first temperature profileinto a first temperature profile frequency domain representation, andtransforming the second temperature profile into a second temperatureprofile frequency domain representation.
 18. The computer-readablestorage medium of claim 10, wherein monitoring the first temperatureprofile and the second temperature profile includes systematicallymonitoring and recording a set of temperature profiles of the computersystem; and wherein the recording process keeps track of the temporalrelationships between events in different temperature profiles.
 19. Anapparatus that determines a flow rate of air along an airflow path in acomputer system, the apparatus comprising: a first temperature sensorlocated in a first position in the airflow path in the computer system;a second temperature sensor located in a second position in the airflowpath in the computer system, wherein the first position is upstream inthe airflow path from the second position, and wherein the firstposition and the second position are separated by a predetermineddistance along the airflow path; a monitoring device configured tomonitor a first temperature profile from the first temperature sensorand a second temperature profile from the second temperature sensor; acomputing mechanism configured to compute a cross-power spectral densitybased on the first temperature profile and the second temperatureprofile; and a determining mechanism configured to determine a flow rateof air in the computer system based on the cross-power spectral density.20. The apparatus of claim 19, wherein the monitoring device includes adevice configured to systematically monitor and record a set temperatureprofiles of the computer system; and wherein the recording process keepstrack of the temporal relationships between events in differenttemperature profiles.